Eric, in brief
1. use висеть when you mean 'be hanging, be suspended"
E.g. when a picture is hanging on the wall...
...or a sportsman is holding the bar (or a rock) and "hangs" still, his feet in the air.
Use вешать when you mean make (something) hanging.
when you are going to hang a picture on the wall.
It is 'be' vs. 'make'.
2. по- (the prefix) has several meanings. Among them:
- Sometimes it is just used to form 'perfective aspect' from 'imperfective':
посмотреть фильм. Or повесить картину на стену.
Sometimes it has a shade of:
"be doing something _for_a_while_, for some time" Often said in a careless, lightminded manner.
Почитать книгу. Я немного почитал и лег спать.
Повисеть. Прежде чем подтянуться он немного повисел и пораскачивался на турнике.